In some emerging Internet data center (IDC) projects, the waste heat dissipated from IT facilities is being captured and supplied to the district heating systems for energy efficiency concerns. From the perspective of electricity consumption and heat production, IDCs can be regarded as energy prosumers, whose spatial and temporal flexibility of energy behaviors is of great significance for the operation of integrated electricity-heat systems (IEHSs). To explore the potential benefits, the required modeling and dispatching techniques are investigated in this paper. Firstly, an Internet-service based energy prosumer model of IDCs is formulated. Especially, the heat production capability is represented considering the complete dynamic heat flow including the heat dissipation, exchange, recovery, and upgrading. And fuzzy parameters are utilized to characterize the uncertainties of the forecasted workloads in advance of the dispatch for IDCs. Moreover, an integrated operation framework for the IDC-IEHS is constructed. Specifically, a hierarchical dispatch scheme is further proposed to achieve privacy-constrained cooperative scheduling between the energy system and IDCs. In the scheme, the energy requirements for IDCs are obtained from the integrated optimal heat and power flow calculation where the temporal scale difference between the electric power and heating systems is considered. The obtained energy requirements are then regarded as the target values for the workload scheduling of IDCs. A deviation correction mechanism is designed to achieve the overall optimality of the IDC-IEHS. Finally, the hydraulicthermal decomposition and trapezoid fuzzy value equivalence methods are used to solve the optimization problems. Simulation results demonstrate that exploiting IDCs as energy prosumers can promote the accommodation of renewables and reduce system cost in the IEHS, as well as improving the self energy efficiency of IDCs.